Hence, the difference in political preferences can be measured by the distance of the two players on this scale.

Here, the parties’ distance is computed as an absolute value of the difference between the parties' preferences. Logically, the closer the preferences (the smaller the distance) between parties, the more likely they are to reach an agreement.
Now, we will apply this model to the coalition formation assuming that the probability that a coalition will be formed (W) depends solely on the distance between the extreme players of that coalition and the parameter u measuring the flexibility of negotiation between players.

The range of W, as in the case of probability should be, is: <0,1>. Understandably, the higher the flexibility of parties, the more likely an agreement is reached. The parameter, however, reflects high flexibility with low values. The higher the u is the more rigid the parties in the negotiation process are ( ). If u is unknown, we assign it value = 1. If the flexibility is fixed, the probability of reaching an argument depends only on the distance between parties’ preferences. According to this logic, as well, two players with identical preferences or infinite negotiational flexibility will always reach an argument (which is quite intuitive). At this moment, we may prove that the probability of building a coalition according to policy closeness condition depends only on the distance between the two extreme players:
W(a,b).W(b,c) = exp(-uda,b).exp(-udb,c) = exp(-u(da,b+db,c)) =
= exp(-uda,c) = W (a,c)
Similarly, these rules apply to n players. The order in which players enters a coalition does not matter.
From a political view, this approach matches reality very narrowly. As the several studies in political change demonstrate, today’s political spectrums can no longer be described by only one dimension – namely, according to the old left-right cleavage. There are already many multidimensional indexes that allow several issues to form the party’s preference, but since their understanding and delineation requires higher mathematical knowledge I will not introduce them in this paper.

4 Conclusion
Defining and measuring the power index of party in the coalition building process is a very difficult and ambiguous task. It has been approached mainly in two ways – the “policy-oriented” and the “policy-blind” (mathematical).
From a political view, several ‘laws’ can be described. Coalitions tend to be minimal winning, minimum sized, preferably with smallest number of parties and with smaller range of political preferences.